Build number 2

Build number 2 is a little better as it focuses on getting FB with ignite.

10/7/13 masteries allow you to get ignite mastery, Strength of Spirit and the mana regen in utility.

This build is more tanky late game also because of the 2 Rod of Ages that are bought bring Ryze's hp up to about 3.5k

This build still does a fair amount of damage but has a hard time getting through late game MR.

Build 3 Skip to this if you want my actualy build

In build 3 I have put the items in order of purchase.
Masteries: I run 9/7/14 masteries for the 15% spell pen, Strength of Spirit which gives 51 hp/5 at end game and i grab mana regen increasing buff duration and 2 points in Swiftness.

> I chose Lich's Bane instead of Banshee's Veil because it gives my combo about 500 more damage per 4-5 seconds than veil and the 7% movement speed allows me to run around fights and kite better while still giving me some MR. So you trade 20 MR, 375hp and spell shield for 500 more damage/5, 7%MS, having your hands glow orange! and ability to push towers better.

When your Tear of the Goddess is max turn it into Archangel's Staff!
Final item in the build is Void Staff because who cares if you have 1k numbers on your spells when the enemy has 100 MR? It's better to see lower numbers but have more actual damage.

Specs of build
Mana at end 5.2k
Ap at end about 420
CDR at end 40%
MS bonus 13.5%
Spell pen- Flat 8.5 and 50%

So you are able to do a lot of damage with all your skills. max CDR for a 15 sec ult and spammable qwe. Ability to actually kite enemies. Lich bane procs to kill towers quicker and to do more damage in fights. 50% spell pen to get threw any MR with ease.

League of Legends is a team based, real time strategy game set in a mythical world of swords & magic where epic battles decide the fate of mystical nations. Game players take on the role of a Summoner who conjures and controls champions to fight for them at the Institute of War. During game play champions gain experience and items to enhance their skills and abilities. How players develop and play their champions can be the difference between a crushing defeat or a glorious victory!